find the exact value of $\\sin^{-1}(-\\frac{1}{2})$.\n$\\sin^{-1}(-\\frac{1}{2})=\\square$\n(type your…
find the exact value of $\\sin^{-1}(-\\frac{1}{2})$.\n$\\sin^{-1}(-\\frac{1}{2})=\\square$\n(type your answer in radians.)
Answer
Explanation:
Step1: Recall the range of the inverse sine function
The range of (y = \sin^{-1}(x)) is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).
Step2: Find the angle in the range with the given sine value
We know that (\sin\left(-\frac{\pi}{6}\right)=-\frac{1}{2}) and (-\frac{\pi}{6}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).
Answer:
(-\frac{\pi}{6})